Dipolar Coupling and Solids NMR
BCMB/CHEM 8190
Liquids v. Solids
One can collect similar spectra
but some tricks are required
13C
solution, sat’d glucose, 8 min
13C
CP-MAS, 30 mg cellulose, 9 min
The Classical Dipole-Dipole Interaction:
z
θ
B0
μ1
θ
r
r
μ2
x
φ
y
E = (μ0/4π)(( μ1· μ2)/r3 – 3(μ1· r)( μ2·r)/r5)
r = i rx + j ry + k rz = i r sinθcosφ + j r sinθsinφ + k r cosθ
Quantum Mechanical Dipolar Coupling
μ = (γh/2π)(i Ix + j Iy + k Iz) = (γh/2π)f(Iz, I+,-)
HD = (μ0γ1γ2h2)/(16π3r3)(A + B + C + D + E + F)
A,B,C .. Grouped by type of operator, 0,1,2 Quantum
A = - Iz1Iz2(3cos2θ - 1), B = (1/4)(I+1I-2 + I-1I+2) (3cos2θ - 1)
………..
E = -(3/4)(I+1I+2)sin2θexp(-2iφ), F = ……..
To First Order Only Iz1Iz2 Term is Important
A doublet would result – much like scalar coupling
but large: as much as -60,000 Hz for a 13C-1H pair.
Splittings are angle dependent – ranging from
-60,000 to +30,000. In a solid all possibilities
superimpose: The result is a powder pattern
Points at 90º on a sphere
are most abundant
D
Other Anisotropies in NMR
H = HCSA + HD + HQ...
All share the following property:
Solution: < 3 cos 2 θ '– 1 > = 0
Solids: (3 cos 2 θ ' – 1) ≠ 0
CSA powder pattern
Techniques in Solids NMR
• Cross Polarization (CP)
• Magic Angle Spinning (MAS)
• High power decoupling
Cross Polarization Improves Sensitivity
Magnetization transfer
via dipolar coupling.
Hartman-Hahn:
γIBI = γSBS
Magic Angle Spinning
•
All interactions can be written in terms of Y20(θ) = (3cos2(θ)–1)/2
•
Y20(θ) can be transformed to another frame using Wigner Rotation
elements: Y20(θ) = Σ2m=-2 D2m0(θ’’,φ’’) Y2m (θ’,φ’)
•
D2m0(θ’’,φ’’) = (4π/5) Y2m (θ’’,φ’’)
•
With rapid averaging over φ’’, all terms except Y20(θ’’) go to zero
•
Selecting θ’’ = 54.7°, all interactions, regardless of θ’ value, are zero
•
(3cos2(θ)–1) = (3cos2(θ’)–1) <3cos2(54.7°)–1> = 0
Dipolar couplings
CSA
Quadrupolar couplings
= 0
φ’’
X
Z
θ’’
θ’
θ
Y
Bo
θ
100 MHz Spectrometer with HFC Transmission-Line Probe
•
100 MHz Spectrometer
High power decoupling
Solution 13C-1H
J
Solid 13C-1H
J + D = ~125 kHz
= ~125 Hz
Cellulose
(10 minute spectra)
What is this peak?
13C
Spinning Sidebands are Frequently Seen
When rotation rate is not >> anisotropies
Resonance position is modulated by rotation
Sidebands at the spinning frequency are produced
There are tricks that remove these:
TOSS – Total Suppression of Spinning Sidebands
180º pulses during rotor cycle dephases sideband
magnetization but preserves center band magnetization
Peptide
1,2-13C2-Gly
(9 minute spectra)
Biomolecular Applications
Spider Silk
Nephila edulis
Nature as Engineer
•
•
•
•
Strongest fiber
β-sheet
Poly-Ala = crystalline
Poly-Gly = amorphous
Spider Silk and SS-NMR
•
•
•
Torsion angle
pairs to resolve
backbone
structure
Ala in two
different
environments
Dynamics
Ψ
Φ
Rhodopsin
• Absorbs light in visible
region
• Binds retinal
Rhodopsin in simulated bilayer
Theoretical and Computational Biophysics Group,
Schulten Laboratory
Univ. Illinois Urbana-Champaign
http://www.blackwellscience.com/matthews/rhodopsin.html
Antibiotics & bacterial growth
Schaefer Laboratory, Washington University, St. Louis, MO
New Solids NMR Assignment Strategies
Parallel Solution Methods
Aliphatic region of the 13C,13C CP MAS PDSD of Zn-MMP-12 (16.4 T,
11.5 kHz MAS frequency, 15 ms mixing time). (Balayssac, Oschkinat,
2007)
Annual Reviews
2D solid-state NMR spectra of
uniformly 15N,13C-labeled Aβ1-40
amyloid fibrils. (a) 2D 13C-13C NMR
spectrum, obtained in a 14.1-T
magnetic field with 13.6-kHz
magic-angle spinning, using a
2.94-ms finite-pulse radiofrequency-driven recoupling
(fpRFDR) sequence for spin
polarization transfer in the mixing
period. (b) 2D 15N-13C spectrum,
obtained with frequency-selective
15N-13C cross-polarization followed
by fpRFDR in the mixing period.
SOLIDS NMR REFERENCES
Ashida, J., Ohgo, K., Komatsu, K., Kubota, A., and Asakura, T. (2003). Determination
of the torsion angles of alanine and glycine residues of model compounds of
spider silk using solid-state NMR methods. J. Biomol. NMR 25, 91-103.
Kim, S.J., Cegelski, L., Studelska, D.R., O'Connor, R.D., Mehta, A.K., and Schaefer,
J. (2002). Rotational-echo double resonance characterization of vancomycin
binding sites in Staphylococcus aureus. Biochemistry 41, 6967-6977.
Grobner, G., Burnett, I.J., Glaubitz, C., Choi, G., Mason, A.J., and Watts, A. (2000).
Observations of light-induced structural changes of retinal within rhodopsin.
Nature 405, 810-813.
Solid-state NMR of matrix metalloproteinase 12: An approach complementary to
solution NMR (2007) Balayssac S, Bertini I, Falber K, Oschkinat, H, et al.
CHEMBIOCHEM 8 486-489.
Solid-State NMR Studies of Amyloid Fibril Structure (2011) Tycko R. Ann. Rev. Phys.
Chem. 62, 279-299.
Recent contributions from solid-state NMR to membrane protein structure and
function, Judge, PJ and Watts, A, (2011) Cur. Opin. Chem. Biol. 15, 690-695.